Answer
$f'(r) = \frac{D}{\sqrt{Dr}}$
For larger reproductive rates $r$, the wave speed $f(r)$ is faster. However, the rate of change of the wave speed with respect to the reproductive rate decreases as the value of the reproductive rate increases.
Work Step by Step
$f(r) = 2\sqrt{Dr}$
We can find the derivative of the wave speed with respect to the reproductive rate:
$f'(r) = 2[\frac{1}{2}(Dr)^{-1/2}]*D$
$f'(r) = \frac{D}{\sqrt{Dr}}$
For larger reproductive rates $r$, the wave speed $f(r)$ is faster. However, the rate of change of the wave speed with respect to the reproductive rate decreases as the value of the reproductive rate increases.
